There is no account of baby Jesus speaking recorded in the Bible.
That's not relevant to your question concerning when the end times started
The arrival of Jesus marked the beginning of the end.
He did all His speaking later when He went in to public ministry and the devil has sought to twist and pervert His teachings ever since including the Lord's teaching ministry that continued after He ascended back to the Father which He taught by the Holy Spirit thru the New Testament writers.
The deception satan is peddling to mankind comes thru so called protestant, catholic, and eastern orthodox churches as well as the ever so popular non denominational churches.
Jesus told us that many would come in His Name and would deceive many so beware of those claiming to be "anointed" to speak in behalf of the Lord who don't teach all of God's Word and who teach the wisdom of men as though it were the wisdom of the Lord which is what these religious organizations are doing.